A tyre changing machine of that kind is known from EP-patent 2 065 230 or EP-patent 2 110 270, for example. When mounting a wheel or a rim/tyre assembly on an automatic tyre changing machine in order to fit or remove a pneumatic tyre to or from a wheel rim of a motor vehicle wheel, the rim is connected to the wheel mounting device in a non-rotatable relationship therewith and in centered relationship with the axis of the wheel by fixing means, in particular clamping means such as a locking pin. A driving pin is provided at the wheel mounting device for engaging with the rim and transmitting torque and rotational motion between the wheel mounting device and the wheel. In some cases, centering and engagement is not automatically achieved by the clamping means and the driving pin, and the operator has to manually adjust the wheel or the rim respectively, or the rim/tyre assembly into the desired position.